Nora Bello's suggestion to consult Walt Stroup's book is excellent. I believe I read this material in it came out came out in 2012, but, surprisingly, I don't have a copy to check my 74-YO memory. (Sorry, Walt, my also o-l-d friend, including a couple of rounds of golf over the years.)

I am, however, 98.6732% sure that he has long advocated using a basic "trick" I proposed >40 years ago called the "exemplary data method." In brief, you create an artificial data set that models your scenario for how Mother Nature and Lady Luck will conspire to produce the data for your proposed study. You then (1) feed these data to your favorite modeling software to produce the likelihood-ratio statistics of interest, then (2) turn those into non-centrality parameter values, and then (3) compute the power probabilities.

Letting the exemplary dataset have N observations give a non-centrality value of lambda(N), a study with cN observations has a non-centrality value of c*lambda(N). One should also do sensitivity analyses by changing the exemplary data in various ways to see how this affects the powers of interest. What all this does is force you to get very involved in the study design and to tailor your statistical plan to the specific research questions.

The same approach is used in Section 6.5 of Agresti's book, Categorical Analysis, 2nd Edition. The example in 6.5.5 is quite simple, so it would be a good place to start--you can check his

computations with yours to make sure you "get it." Those who want to dive more deeply might check out

Shieh, G. (2000). On power and sample size calculations for likelihood ratio tests in generalized linear models. Biometrics, 56(4):1192–6.

Actually, I now advocate using study-specific Monte Carlo simulations to examine how a few tailored confidence intervals behave under reasonable exemplary dataset scenarios, but that's a topic for another day, week, month, year, or even a career.

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Ralph O'Brien

Professor of Biostatistics (officially retired; still keenly active)

Case Western Reserve University

http://rfuncs.weebly.com/about-ralph-obrien.html------------------------------

Original Message:

Sent: 05-18-2023 15:40

From: Brandy Sinco

Subject: Power for Generalized Linear Model, Binary Outcome, Longitudinal Data, Clustered by Hospital

Dear ASA:

Does anyone have a reference (text book or article) that describes how to calculate the power and sample size for:

Binary data (Outcome is rate of a particular surgical procedure)

Longitudinal over 6 years in increments of year

Clustered by Hospital, approximately 1500 hospitals

SAS preferred, although R or Stata also fine.

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Brandy Sinco, BS, MA, MS

Statistician Senior

Michigan Medicine

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